Question

compute the slopes for the two given functions and determine which function has a greater rate of change.
(i)table function
(ii)graph function

\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline 3 & 6 \\\\ \\hline 4 & 8 \\\\ \\hline 5 & 10 \\\\ \\hline 6 & 12 \\\\ \\hline \\end{array}$$

\bigcirc$ the graph function has a greater rate of change.
\bigcirc$ the table function has a greater rate of change.

Explanation:

Calculate the slope of the table function

Using the Slope of a Linear Function knowledge point

$$ m_{\text{table}} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 6}{4 - 3} = 2 $$

Calculate the slope of the graph function

Using the Slope of a Linear Function knowledge point

$$
LATEXBLOCK0
$$

Compare the rates of change

Using the Rate of Change Comparison knowledge point

$$
LATEXBLOCK1
$$

Answer:

• The graph function has a greater rate of change.
• The table function has a greater rate of change. (Correct answer)